You are kidding, right? Both are Constitutional. The 16th Amendment reads: "The Congress shall have power to lay and collect taxes on income, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration." There is nothing that requires the "tax on income" be deducted in a paticular manner. A sales tax is a tax on income, as is a flat tax.
Should point out too -- that to argue against the DNC -- that they have the power and are not required to do it one way or the other. I imagine the DNC will have talking heads come out and tell Americans that its impossible because the constitution "requires" income tax collection.